I’m not sure if that’s correct or not can you make sure for me ### Solving Homogeneous System of Linear EquationsTo solve the problem, we need to find the general solution of the homogeneous system of linear equations given below. The solution should be provided as a vector.#### System of Linear Equations:\[ \begin{aligned}&x_1 + 2x_2 - 3x_3 = 0 \\&4x_1 + 7x_2 - 9x_3 = 0 \\&-x_1 - 3x_2 + 6x_3 = 0 \\\end{aligned}\]#### Answer Choices:1. \[\left[\begin{array}{c}x_1 \\x_2 \\x_3 \\\end{array}\right]=x_3 \left[\begin{array}{c}-3 \\3 \\0 \\\end{array}\right]\]2. \[\left[\begin{array}{c}x_1 \\x_2 \\x_3 \\\end{array}\right]=x_3 \left[\begin{array}{c}-3 \\3 \\1 \\\end{array}\right]\] (Correct Answer)3. \[\left[\begin{array}{c}x_1 \\x_2 \\x_3 \\\end{array}\right]=\left[\begin{array}{c}-3 \\3 \\1 \\\end{array}\right]\] 4. \[\left[\begin{array}{c}x_1 \\x_2 \\x_3 \\\end{array}\right]=x_3 \left[\begin{array}{c}3 \\-3 \\1 \\\end{array}\right]\]Choose the correct vector that represents the general solution to the given system of linear equations.

Answered: Image /qna-images/answer/c14dec42-b6aa-4b56-8602-9aefa47d3b57.jpg

Answered: Solve the problem. Find the general…

Solve the problem. Find the general solution of the homogen X1 + 2x2 3x3 = 0 4x1 + 7x29x3 = 0 -X1 - 3x2 + 6x3 = 0 Ox1 x2 = x3 3 x3 0 x1 -3 x2 = x3 3 1 x3 Ox1 x2 = x3 Ox1 -3 3 1 3 x2 = X3 -3 1 x3 2

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Matrices And Determinants

Section: Chapter Questions

Problem 15T: One hundred liters of a 50% solution is obtained by mixing a 60% solution with a 20% solution. Use a...

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Question

I’m not sure if that’s correct or not can you make sure for me

### Solving Homogeneous System of Linear Equations

To solve the problem, we need to find the general solution of the homogeneous system of linear equations given below. The solution should be provided as a vector.

#### System of Linear Equations:
\[
\begin{aligned}
&x_1 + 2x_2 - 3x_3 = 0 \\
&4x_1 + 7x_2 - 9x_3 = 0 \\
&-x_1 - 3x_2 + 6x_3 = 0 \\
\end{aligned}
\]

#### Answer Choices:

1. \[
\left[
\begin{array}{c}
x_1 \\
x_2 \\
x_3 \\
\end{array}
\right]
=
x_3
\left[
\begin{array}{c}
-3 \\
3 \\
0 \\
\end{array}
\right]
\]

2. \[
\left[
\begin{array}{c}
x_1 \\
x_2 \\
x_3 \\
\end{array}
\right]
=
x_3
\left[
\begin{array}{c}
-3 \\
3 \\
1 \\
\end{array}
\right]
\] (Correct Answer)

3. \[
\left[
\begin{array}{c}
x_1 \\
x_2 \\
x_3 \\
\end{array}
\right]
=
\left[
\begin{array}{c}
-3 \\
3 \\
1 \\
\end{array}
\right]
\]

4. \[
\left[
\begin{array}{c}
x_1 \\
x_2 \\
x_3 \\
\end{array}
\right]
=
x_3
\left[
\begin{array}{c}
3 \\
-3 \\
1 \\
\end{array}
\right]
\]

Choose the correct vector that represents the general solution to the given system of linear equations.

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